System of equations with squared floor function
Source: Czech and Slovak Olympiad 1975, National Round, Problem 2
July 20, 2024
algebrasystem of equationsfloor functioninequalitiesboundedsquarefunction
Problem Statement
Show that the system of equations
\begin{align*}
\lfloor x\rfloor^2+\lfloor y\rfloor &=0, \\
3x+y &=2,
\end{align*}
has infinitely many solutions and all these solutions satisfy bounds
\begin{align*}
0<\ &x <4, \\
-9\le\ &y\le 1.
\end{align*}